The effective modeling of electromagnetic waves on unbounded domains by numerical techniques, such as the finite difference or the finite element method, is dependent on the particular absorbing boundary condition used to truncate the computational domain. In 1994, J. P. Berenger created the perfectly matched layer (PML) technique for the reflection-less absorption of electromagnetic waves in the time domain. The PML is an absorbing layer that is placed around the computational domain of interest in order to attenuate outgoing radiation. Berenger showed that his continuous PML model allowed perfect transmission of electromagnetic waves across the interface of the computational domain regardless of the frequency, polarization or angle of incidence of the waves. The waves are then attenuated exponentially with respect to depth into the absorbing layers.
The properties of the continuous PML model have been studied extensively and are well documented. Since its original inception in 1994, the PML technique has extended its applicability to areas other than computational electromagnetics such as acoustics and elasticity. In this talk, I will describe the original split field PML technique of Berenger as well as some of the popular modifications of the original method. The mathematical and numerical aspects of the problem will be discussed. Finite difference and mixed finite element methods will be applied to the discretization of the PML in the time domain. The discrete PML will be used to demonstrate wave propagation on unbounded domains in two dimensions.